However, looking at individual distributions of angles alone does not capture the fact that these angles are not independently distributed, but rather exhibit significant correlations. A Ramachandran plot, which plots the frequency of co-occurrence between the dihedrals \((\phi , \psi )\) , is commonly used to illustrate these correlations between angles [1]}. Figure REF  shows the Ramachandran plot for chains with fewer than 128 residues in the test set, as well as that for our 780 generated structures. The Ramachandran plot for natural structures (Figure REF ) contains three major concentrated regions corresponding to right-handed \(\alpha \)  helices, left-handed \(\alpha \)  helices, and \(\beta \)  sheets. All three of these regions are recapitulated in our generated structures (Figure REF ). In other words, FoldingDiff is able to generate all three major secondary structure elements in protein backbones. Furthermore, we see that our model correctly learns that right-handed \(\alpha \)  helices are much more common than left-handed \(\alpha \)  helices [2]}. Prior works that use equivariant networks, such as [3]}, cannot differentiate between these two types of helices due to network equivariance to reflection. This concretely demonstrates that our internal angle formulation leads to improved handling of chirality (i.e., the asymmetric nature of proteins) in generated backbones.
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